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Search: id:A066730
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| A066730 |
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Numbers with ever-increasing minimal-square-deniers. |
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2
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| 2, 3, 12, 21, 60, 184, 280, 364, 1456, 3124, 5236, 17185, 25249, 49504, 233776, 364144, 775369, 3864169, 8794864
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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The Jacobi of modular reductions of a number is often used by a bignum library to give a quick (negative) answer to the question of whether an integer is an exact square. This sequence gives the cutoffs for ever-increasing numbers of required modular tests, on the assumption that one is avoiding a brute force square-root/square/compare. All terms to 8794864 found by Jack Brennen.
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LINKS
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J. Brennan, discussion about issquare() tests without use of sqrt() on Caldwell's 'primenumbers' list
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EXAMPLE
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2 is 'square-denied' by 3, as 2 is not a quadratic residue mod 3 3 is square-denied by 2^2=4, but not by any lower prime power (2 or 3) 12 has 5 as its minimal square-denier (0 mod 2, 0 mod 3, 0 mod 4 all QRs) 21 has 2^3=8 as its minimal square-denier. (note that 24 has 7 as its minimal square-denier, the first number with that property, but it is larger than 21)
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CROSSREFS
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Sequence in context: A124261 A077755 A018883 this_sequence A061268 A122604 A024780
Adjacent sequences: A066727 A066728 A066729 this_sequence A066731 A066732 A066733
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KEYWORD
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more,nonn
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AUTHOR
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Phil Carmody (pc+oeis(AT)asdf.org), Jan 15 2002
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